In a recent poll of 500 13-year-olds, many indicated to enjoy their relationships with their parents. Suppose that 200 of the 13-year olds were boys and 300 of them were girls. We wish to estimate the difference in proportions of 13-year old boys and girls who say that their parents are very involved in their lives. In the sample, 93 boys and 172 girls said that their parents are very involved in their lives. What is a 96% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)? (a) Calculate a 95% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)?
(b) Interpret your interval calculated above.

CI 96 %  =  ( - 0.1128  ; 0.0728 )

CI 95%  =  ( - 0.1087 ; 0.6878 )

The two intervals contain 0 value therefore we can support that there is not statistics difference between the two groups with confidence level of 96 % and  95%

Step-by-step explanation:

Boys sample:

sample size   n₁  = 200

x₁  number of boys saying their parents are very involved in their lives

=  93

p₁ = x₁/n₁   =  93/200  =  0.465  then  q₁ =  1  -  p₁   q₁ = 1 - 0.465  q₁ = 0.535

Girls sample

sample size   n₂  = 300

x₂  number of girls saying their parents are very involved in their lives

=  172

p₂  =  x₂/n₂  =  172/ 300  =  0.573 then  q₂ = 1 -0.573  q₂ =  0.427

CI 96 %      α = 4 %  α = 0.04    α/2 = 0.02  

p₁  -  p₂  =  0.465 -  0.573  = - 0.168

CI 96 %   =  (  p₁  -  p₂ ) ±  z(c) * SE

z(c)  for  α  =  0.02       z(c)  =  - 2.05

SE = √ (p₁*q₁)/n₁  +  (p₂*q₂)/n₂

SE = √ ( 0.465*0.535)/200  +  (0.573*0.427)/300

SE =  √  0.00124  +  0.000815    

SE =  √  0.00205

SE =   0.0453

CI 96 %  =  (  -0.02  ±  ( 2.05 * 0.0453 ) )

CI 96 %  =  (  -0.02  ±  ( 0.0928 ))

CI 96 %  =  ( - 0.1128  ; 0.0728 )

a) CI 95%  α =  5 %   α = 0.05     α/2 =  0.025

SE = 0.0453

z(c) for  0.025 is from z-table   z(c)  =  1.96

CI 95%  =  ( - 0.02 ±  1.96 * 0.0453)

CI 95%  =  ( - 0.02 ± 0.08878 )

CI 95%  =  ( - 0.1087 ; 0.6878 )

is it 35

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is